Projection screen and projection display device

ABSTRACT

A projection screen  111  comprises a total reflection prism lens  114  and a lenticular lens  115  provided on the viewer&#39;s side of the total reflection prism lens  114 . The total reflection prism lens  114  has a plurality of unit prisms  113  on its back surface (the outermost plane of incidence) on which imaging light L is incident. Each unit prism  113  has an apical angle λ that corresponds to the angle between the plane of incidence  113   a  and the plane of total reflection  113   b , and the apical angles λ of the unit prisms  113  vary with the position of each unit prism  113  on the screen plane. In particular, the unit prisms  113  have apical angles λ varying continuously from 30° to 45° so that the apical angles λ on the side distant from the center O of the concentric circles are greater than the apical angles λ on the side close to this center O.

FIELD OF THE INVENTION

The present invention relates to a projection screen, especially aprojection screen suitable for viewing imaging light that is obliquelyprojected on the screen from a cellular-structured imaging light sourcesuch as an LCD (Liquid Crystal Display) or DMD (Digital Micro-mirrorDevice), and to a projection display comprising the projection screen.

BACKGROUND ART

There has conventionally been known, as a display of rear projectiontype (rear projection type television), a projection display using threeCRTs of red, green and blue colors as an imaging light source, in whichimaging light emitted from such an imaging light source is projected onthe back surface of a transmission projection screen to produce animage, which is viewed from the viewer's side.

A projection screen for use in such a projection display is usuallycomposed of a Fresnel lens sheet and a lenticular lens sheet, and allowsimaging light emitted from an imaging light source to form an image andto emerge toward viewers as directional diffused light.

Specifically, for example, a projection screen 300 comprises, as shownin FIG. 20, a Fresnel lens sheet 301 having a circular Fresnel lens 302formed on its emergent side surface, and, on the viewer's side of theFresnel lens sheet 301, a lenticular lens sheet 303 having a lenticularlens 304 for horizontal diffusion formed on its incident side surface.On the emergent side surface of the lenticular lens sheet 303 areprovided lenses 305 from which light emerges and black stripes 306.

Of these, the Fresnel lens 302 on the Fresnel lens sheet 301 can beobtained by grooving a transparent resin material, such as an acrylicresin, at a predetermined angle and at a predetermined pitch, and hasthe function of condensing, toward the viewer's side, radially diffusedimaging light that is emitted from an imaging light source (not shown inthe figure) placed at the rear of the Fresnel lens sheet 301. Thelenticular lens 304 on the lenticular lens sheet 303 can be obtained byforming cylindrical unit lenses so that they extend on one planeregularly and longitudinally, and has the function of diffusing, chieflyin the horizontal direction, the imaging light condensed by the Fresnellens sheet 301 to let the light emerge as directional diffused light inthe horizontal direction.

In the meantime, in place of the above-described projection displayusing three CRTs of red, green and blue colors, a projection display ofsingle lens mode which uses a cellular-structured imaging light sourcesuch as an LCD or DMD and in which imaging light emitted from such animaging light source is projected on the back surface of a transmissionprojection screen, the produced image being viewed from the viewer'sside, has been increasingly demanded in recent years.

Heretofore, the projection mode usually adopted in such a projectiondisplay of single lens mode is that imaging light is projected on theprojection screen from its rear almost vertically to the projectionscreen. The drawback of a projection display of this mode has been thatsince it requires a depth nearly equal to that of a conventional CRTprojection display, it cannot be made smaller.

Under these circumstances, there has been proposed, as one of projectiondisplays, a projection display in which imaging light emitted from animaging light source is obliquely projected on a projection screen inorder to make the display considerably smaller than conventional oneswithout impairing image quality (see Japanese Laid-Open PatentPublications No. 208041/1986 and No. 180967/2000).

Such a projection display has, on its incident side surface, a group ofunit prisms with triangular cross sections (total reflection prism lens)as an optical means of condensing imaging light obliquely incident onthe projection screen; the first plane (plane of incidence) of each unitprism refracts the incident imaging light, and the second plane (planeof total reflection) of the unit prism then totally reflects therefracted light to let the reflected light emerge from the emergent sidesurface of the projection display.

In the projection screen having such a total reflection prism lens, inthe area on the side close to the imaging light source (in the casewhere the unit prisms concentrically extend around the center of theconcentric circles that is not on the screen plane, in the area on theside close to this center of the concentric circles) in which the angleof incidence of imaging light (the angle of imaging light with thescreen plane) gets smaller, part of imaging light incident on the planeof incidence 311 a of each unit prism 311 of the total reflection prismlens 310 is not totally reflected at the plane of total reflection 311 bof the unit prism 311 and, as shown in FIG. 21, passes through thisplane to become stray light, causing such troubles as the formation ofdouble image (ghost). In FIG. 21, reference character L11 denotes thelight path of a component of imaging light that becomes ordinary light,and reference character L12 denotes the light path of a component ofimaging light that becomes stray light. The amount of stray light thusproduced is greater when each unit prism 311 has a larger apical angleλ, and is smaller when each unit prism 311 has a smaller apical angle λ.

On the other hand, in the projection screen having the above-describedtotal reflection prism lens, in the area on the side distant from theimaging light source (in the case where the unit prisms concentricallyextend around the center of the concentric circles that is not on thescreen plane, in the area on the side distant from this center of theconcentric circles) in which the angle of incidence of imaging light isgreat, each unit prism 311 has a smaller apical angle λ, and its planeof incidence 311 a gets reverse tapered, as shown in FIG. 22. Therefore,there has been such a problem that part of imaging light incident on theplane of incidence 311 a of each unit prism 311 is totally reflected atthe plane of total reflection 311 b of the unit prism 311 and is thenreflected again at the plane of incidence 311 a to become stray light,causing imaging light loss. In FIG. 22, reference character L21 denotesthe light path of a component of imaging light that becomes ordinarylight, and reference character L22 denotes the light path of a componentof imaging light that becomes stray light. Further, there has been sucha problem that, if the planes of incidence 311 a of the unit prisms 311are reverse tapered, it becomes difficult to make a mold for use in themolding of the unit prisms 311 and also to release the unit prisms fromthe mold in the lens molding process. Furthermore, in the case where themold for use in the molding of the unit prisms 311 is produced bycutting a mold material, it is difficult to shape the moldcorrespondingly to the reverse tapered planes of incidence 311 a of theunit prisms 311, and, moreover, the planes of incidence 311 a of theunit prisms 311 become rough surfaces with flaws created in the courseof cutting. A problem with this case has been as follows: both the areain which the planes of incidence 311 a of the unit prisms 311 are mirrorsurfaces and the area in which the planes of incidence 311 a of the unitprisms 311 are rough surfaces are to exist on the screen plane, so thatthe image produced on the screen plane appears differently at theboundary between these two areas and is thus observed as being uneven.

Thus, the conventional projection screens have the following drawback:since they have narrow allowable ranges of the angle of incidence ofimaging light and tend to cause imaging light loss due to the productionof stray light or the like, they easily undergo lowering of surfacebrightness or contrast.

SUMMARY OF THE INVENTION

The present invention has been accomplished in the light of theabove-described drawback in the background art. An object of the presentinvention is to provide, by increasing the allowable range of the angleof incidence of imaging light that is a range in which imaging lightloss due to the production of stray light or the like is not caused, aprojection screen and a projection display that can display, withoutundergoing lowering of surface brightness or contrast, an image withhigh quality comparable to an image that is obtained when imaging lightis projected on a projection screen almost vertically from an imaginglight source.

The present invention provides a projection screen that allows imaginglight obliquely projected from a projection optical system placed at therear side of the projection screen to emerge toward the viewer's side ofthe projection screen, comprising a total reflection prism lens having aplurality of unit prisms provided on its back surface on which imaginglight is incident, each unit prism having a first plane that refractsthe incident light and a second plane that totally reflects the lightrefracted at the first plane, wherein each unit prism has an apicalangle that corresponds to the angle between the first and second planes,and the apical angles of the unit prisms vary with the position of eachunit prism on the screen plane.

In the present invention, it is preferable that the unit prismsconcentrically extend around the center of the concentric circles thatis not on the screen plane. Further, it is preferable that the unitprisms be made to have apical angles varying so that the apical angleson the side distant from the center of the concentric circles aregreater than the apical angles on the side close to the center of theconcentric circles. Furthermore, it is preferable that the unit prismshave apical angles varying from 30° to 45°. It is also preferable thatthe unit prisms have apical angles that vary continuously as theposition of the unit prism varies from the side close to the center ofthe concentric circles to the side distant from this center.

In addition, in the present invention, it is preferable that the totalreflection prism lens has: a first apical-angle-fixed area in which theunit prisms have apical angles fixed at a predetermined first angle; asecond apical-angle-fixed area whose location is different from that ofthe first apical-angle-fixed area and in which the unit prisms haveapical angles fixed at a predetermined second angle that is differentfrom the first angle; and an apical-angle-varying area that is situatedbetween the first and second apical-angle-fixed areas and in which theunit prisms have apical angles varying between the first and secondangles with the position on the screen plane.

In the above case, it is preferable that the above-describedapical-angle-varying area comprises a first apical-angle-varying part inwhich the unit prisms have apical angles that vary as only the anglebetween the first plane of the unit prism and the screen plane varies,with the angle between the second plane of the unit prism and the screenplane remaining unchanged. Further, it is preferable that theapical-angle-varying area further comprises a secondapical-angle-varying part that is situated between the firstapical-angle-varying part and the first apical-angle-fixed area and inwhich the unit prisms have apical angles that vary as both the anglebetween the first plane of the unit prism and the screen plane and theangle between the second plane of the unit prism and the screen planevary; and a third apical-angle-varying part that is situated between thefirst apical-angle-varying area and the second apical-angle-fixed areaand in which the unit prisms have apical angles that vary as both theangle between the first plane of the unit prism and the screen plane andthe angle between the second plane of the unit prism and the screenplane vary.

Furthermore, in the present invention, it is preferable that the firstplane of each unit prism has a draft angle of 0° or more to theperpendicular to the screen plane. Moreover, it is preferable that thefirst planes of the unit prisms have surface roughness that is uniformover the entire screen plane.

Furthermore, in the present invention, it is preferable that theprojection screen further comprises a lenticular lens for diffusinglight that has passed through the total reflection prism lens, providedon the viewer's side of the total reflection prism lens.

In this case, it is preferable that the lenticular lens has a pluralityof unit lenses with half-elliptic or trapezoidal cross sections.

Preferably, the unit lenses with trapezoidal cross sections are arrangedso that the lower base and upper base of each trapezoid face to theincident side and the emergent side, respectively; portions withV-shaped cross sections are created between each two neighboring unitlenses; the unit lenses are made from a material having a predeterminedrefractive index; those portions created between each two neighboringunit lenses are made from a material having a refractive index that islower than that of the material for the unit lenses; and the interfacesbetween the unit prisms and the portions created between each twoneighboring unit prisms allow light to be totally reflected. Further, itis preferable that the portions with V-shaped cross sections have thelight-absorbing property of absorbing light entering from the viewer'sside of the projection screen. Furthermore, it is preferable that theportions with V-shaped cross sections be made from a resin mixed withlight-absorbing particles.

Furthermore, in the present invention, it is preferable that the totalreflection prism lens and the lenticular lens be integrally made as onesheet.

Furthermore, in the present invention, it is preferable that theprojection screen further comprises a diffusing sheet for diffusinglight that has passed through the total reflection prism lens (or boththe total reflection prism lens and the lenticular lens), provided onthe viewer's side of the total reflection prism lens (or the lenticularlens).

Furthermore, in the present invention, it is preferable that theprojection screen further comprises a functional layer comprising atleast one layer selected from the group consisting of an antireflectionlayer, a hard coat layer, an antistatic layer, an anti-glaring layer, astain-resistant layer, and a sensor layer.

The present invention also provides a projection display comprising theabove-described projection screen and a projection optical system forobliquely projecting imaging light on the projection screen.

According to the present invention, in a projection screen on whichimaging light is obliquely projected from a projection optical systemthat is placed at the rear side of the projection screen, by providing atotal reflection prism lens having a plurality of unit prisms on itsback surface on which imaging light is incident, it is possible tocorrect, only on the incident side (back surface side), the optical axisof imaging light obliquely projected from the projection optical systemand let the imaging light emerge toward the viewer's side. In thepresent invention, the unit prisms are made to have apical anglesvarying with the position on the screen plane. Specifically, forexample, in the case where the unit prisms extend concentrically aroundthe center of the concentric circles that is not on the screen plane,the apical angles of the unit prisms are varied within a certain anglerange (e.g., 30° or more and 45° or less) so that the apical angles onthe side distant from the center of the concentric circles are greaterthan the apical angles on the side close to the center of the concentriccircles. Namely, in the area on the side close to the projection opticalsystem in which the angle of incidence of imaging light is small, theunit prisms are made to have smaller apical angles, while in the area onthe side distant from the projection optical system in which the angleof incidence of imaging light is great, the unit prisms are made to havegreater apical angles. For this reason, it is possible to increase theallowable range of the angle of incidence of imaging light that is arange in which imaging light loss due to the production of stray lightor the like is not caused, and is thus possible to obtain a projectionscreen and a projection display that can display, without undergoinglowering of surface brightness or contrast, an image with high qualitycomparable to an image that is obtained when imaging light is projectedon a projection screen almost vertically from a projection opticalsystem.

Further, according to the present invention, by providing, on the totalreflection prism lens, a first apical-angle-fixed area in which the unitprisms have apical angles fixed at a predetermined first angle, a secondapical-angle-fixed area whose location is different from that of thefirst apical-angle-fixed area and in which the unit prisms have apicalangles fixed at a predetermined second angle that is different from thefirst angle, and an apical-angle-varying area that is situated betweenthe first and second apical-angle-fixed areas and in which the unitprisms have apical angles varying between the first and second angleswith the position on the screen plane, it is possible to vary the apicalangles of the unit prisms of the total reflection prism lens not overthe entire screen plane but only partially. By this, it becomes possibleto easily make a mold for use in the molding of the total reflectionprism lens, and a projection screen and a projection display, bothcapable of ensuring high image quality, can thus be obtained moreinexpensively.

Furthermore, according to the present invention, by providing, in theapical-angle-varying area on the total reflection prism lens, a firstapical-angle-varying part in which the unit prisms have apical anglesthat vary as only the angle between the first plane of the unit prismand the screen plane varies, with the angle between the second plane ofthe unit prism and the screen plane remaining unchanged, and a secondapical-angle-varying part and a third apical-angle-varying part betweenthe first apical-angle-varying part and the first apical-angle-fixedarea and between the first apical-angle-varying part and the secondapical-angle-fixed area, respectively, in which the unit prisms haveapical angles that vary as both the angle between the first plane andthe screen plane and the angle between the second plane and the screenplane vary, it is possible to further make the boundaries between theabove areas appear unclear, and is thus possible to attain higher imagequality.

Furthermore, according to the present invention, by making the firstplane of each unit prism have a draft angle of 0° or more to theperpendicular (normal) to the screen plane, it is possible to preventproduction of stray light, and is thus possible to prevent imaging lightloss. In addition, in this case, since the mold for use in the moldingof the unit prisms includes no reverse tapered portions, it is easy tomake the mold, and, moreover, the unit prisms can be easily releasedfrom the mold in the lens molding process.

Furthermore, according to the present invention, by making the surfaceroughness of the first planes of the unit prisms uniform over the entirescreen plane, it is possible to prevent occurrence of unevenness in animage on the screen plane so that a high-quality image can be viewed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic perspective view showing a projection displaycomprising a projection screen according to the first embodiment of thepresent invention;

FIG. 2 is a perspective view showing the principal part of theprojection screen shown in FIG. 1;

FIG. 3 is an illustration for explaining the light path of imaging lightin the total reflection prism lens of the projection screen shown inFIG. 1;

FIG. 4 is a diagram for explaining the relationship between the apicalangle of each unit prism and the angle of incidence of imaging light inthe total reflection prism lens of the projection screen shown in FIG.1;

FIG. 5 is a diagram for explaining the relationship between the positionand apical angle of each unit prism in the total reflection prism lensof the projection screen shown in FIG. 1;

FIGS. 6A and 6B are views for explaining the first modification of theprojection screen shown in FIGS. 1 to 5;

FIG. 7 is a diagram for explaining the relationship between the positionand apical angle of each unit prism in the total reflection prism lensof the projection screen shown in FIGS. 6A and 6B;

FIG. 8 is a diagram showing the relationship between the angle ofincidence of imaging light and the lens angle of each unit prism in thetotal reflection prism lens of the projection screen shown in FIGS. 6Aand 6B;

FIGS. 9A and 9B are views for explaining the second modification of theprojection screen shown in FIGS. 1 to 5;

FIG. 10 is a diagram for explaining the relationship between theposition and apical angle of each unit prism in the total reflectionprism lens of the projection screen shown in FIGS. 9A and 9B;

FIG. 11 is a diagrammatic perspective view showing a projection displaycomprising a projection screen according to the second embodiment of thepresent invention;

FIG. 12 is a perspective view showing the principal part of theprojection screen shown in FIG. 11;

FIG. 13 is a sectional view taken along line XIII-XIII in FIG. 12;

FIG. 14 is a view showing the first assembly example of a projectiondisplay comprising a projection screen according to the first or secondembodiment of the present invention;

FIG. 15 is a view showing the second assembly example of a projectiondisplay comprising a projection screen according to the first or secondembodiment of the present invention;

FIG. 16 is a view showing the third assembly example of a projectiondisplay comprising a projection screen according to the first or secondembodiment of the present invention;

FIG. 17 is a diagram showing the relationship between the position andapical angle of each unit prism in the total reflection prism lenses inExamples 1 to 3;

FIG. 18 is a diagram showing the relationship between the position andapical angle of each unit prism (the relationship between them in thevicinity of the area in which the apical angles of the unit prisms vary)in the total reflection prism lenses in Examples 4 and 5;

FIG. 19 is a diagram showing the relationship between the position andlens angle of each unit prism (the relationship between them in thevicinity of the area in which the apical angles of the unit prisms vary)in the total reflection prism lenses in Examples 4 and 5;

FIG. 20 is a view showing an example of a projection screen comprising aconventional Fresnel lens sheet;

FIG. 21 is an illustration for explaining the light path of imaginglight, when the unit prisms have great apical angles, in a projectionscreen comprising a total reflection prism lens; and

FIG. 22 is an illustration for explaining the light path of imaginglight, when the unit prisms have small apical angles, in a projectionscreen comprising a total reflection prism lens.

DETAILED DESCRIPTION OF THE INVENTION

By referring to the accompanying drawings, embodiments of the presentinvention will be described hereinafter.

First Embodiment

First of all, a projection screen according to the first embodiment ofthe present invention and a projection display comprising it will bedescribed with reference to FIGS. 1 to 10.

As shown in FIG. 1, a projection display 100 according to the firstembodiment of the present invention comprises a projection screen 111and a projection optical system 112 from which imaging light L isobliquely projected on the projection screen 111. The projection opticalsystem 112 comprises an imaging light source composed of an LCD, DMD, orthe like, and an optical system for spreading the imaging light emittedfrom the imaging light source.

The projection screen 111 is for letting imaging light L obliquelyprojected from the projection optical system 112 placed at its rear sideemerge toward the viewer's side, and comprises a total reflection prismlens 114, and a lenticular lens 115 provided on the viewer's side of thetotal reflection prism lens 114.

Of these components, the total reflection prism lens 114 is forrefracting and condensing imaging light L projected from the projectionoptical system 112, and, as shown in FIG. 2, has a plurality of unitprisms 113 on its back surface (the outermost plane of incidence) onwhich the imaging light L is incident.

Each unit prism 113 has a plane of incidence (first plane) 113 a thatrefracts incident light, and a plane of total reflection (second plane)113 b that totally reflects the light refracted at the plane ofincidence 113 a. The unit prism 113 can therefore refract and totallyreflect obliquely projected imaging light L to let the light travel inthe direction nearly vertical to the screen plane. The unit prisms 113are made as prisms in the shape of circular arcs extendingconcentrically around the center O of the concentric circles that is noton the screen plane (see FIG. 1). Specifically, for example, it ispreferable that the prism pitch of the unit prisms 113 be from 100 to200 μm and that the height of each unit prism 113 be from 150 to 300 μm.

Each unit prism 113 has an apical angle λ that corresponds to the anglebetween the plane of incidence 113 a and the plane of total reflection113 b, and the apical angles λ of the unit prisms 113 vary according tothe position of each unit prism 113 on the screen plane. In particular,it is preferable that the unit prisms 113 have apical angles λcontinuously varying from 30° to 45° so that the apical angles λ on theside distant from the center O of the concentric circles (the upper sidein the figure) are greater than the apical angles λ on the side close tothe center O of the concentric circles (the lower side in the figure).

On the other hand, the lenticular lens 115 is for horizontally diffusinglight that has passed through the total reflection prism lens 114, andhas a plurality of cylindrical unit lenses 116 on its incident side fromwhich imaging light L enters. Specifically, for example, each unit lens116 has preferably a half-elliptic cross section with a transversediameter of 140 μm and a longitudinal diameter of 100 μm; the lens pitchis preferably 140 μm; the height of each unit lens is preferably 50 μm;and the angle of horizontal diffusion is preferably from 20 to 50° whenexpressed by half angle (the angle at which the brightness observed froma certain direction becomes a half of the brightness observed from thefront).

As shown in FIGS. 1 and 2, the total reflection prism lens 114 and thelenticular lens 115 are made as separate sheets (a prism sheet and alenticular lens sheet). Moreover, in FIGS. 1 and 2, the total reflectionprism lens 114 and the lenticular lens 115 are, for easy understanding,depicted as being separated more than the actual distance between them.

Next, the light path of imaging light L in the total reflection prismlens 114 of the projection screen 111 shown in FIG. 1 will be explainedwith reference to FIG. 3.

As shown in FIG. 3, imaging light L emitted from the projection opticalsystem (see reference numeral 112 in FIG. 1) is incident on the plane ofincidence 113 a of each unit prism 113 of the total reflection prismlens 114 at an angle of incidence θ₁ that varies depending upon theposition of the unit prism 113 on the screen plane. It is preferablethat the angle of incidence θ₁ at which imaging light L is incident onthe unit prism situated at the edge of the screen plane on the sideclose to the projection optical system (on the side close to the centerO of the concentric circles) be made 35° or more (preferably 45° ormore) and 50° or less.

The imaging light L incident on the plane of incidence 113 a of eachunit prism 113 is refracted at the plane of incidence 113 a and thentotally reflected at the plane of total reflection 113 b, and thistotally reflected light travels toward the viewer's side in thedirection nearly vertical to the screen plane.

To attain the above-described light path of imaging light L, the shapeof each unit prism 113 is determined according to the angle of incidenceθ₁ of imaging light L. Specifically, when the lens angle of each unitprism 113 (the angle between the plane of total reflection 113 b and thescreen plane) is denoted by φ; the apical angle of the unit prism 113,by λ; the refractive index of the material for the total reflectionprism lens 114, by n; and the angle between imaging light L reflected atthe plane of total reflection 113 b of the unit prism 113 and the normalto the screen plane, by θ₄, the shape of the unit prism 113 can bedetermined by the following Eq. (1):tan φ={n sin(λ+θ₄)+sin(λ+θ₁)}/{n cos(λ+θ₄)−cos(λ+θ₁)}  (1)

Further, if the emergent side surface of the total reflection prism lens114 is flat, the following Eq. (2) holds between the angle θ₄ at whichimaging light L travels in the total reflection prism lens 114 and theangle θ₅ at which the imaging light L emerges from the total reflectionprism lens 114:sin θ₄=sin θ₅ /n.  (2)

When the angle between the plane of incidence 113 a of each unit prism113 and the normal to the screen plane is denoted by γ, this angle ispreferably as follows:γ=φ+λ−π/2≧0.  (3)

The reason for this is as follows: when the angle γ of the plane ofincidence 113 a of each unit prism 113 is negative, the plane ofincidence 113 a of the unit prism 113 gets reverse tapered; in thiscase, it is difficult to make a mold for use in the molding of the unitprisms 113 and also to obtain the unit prisms 113 by molding using amold.

The lens angle φ of each unit prism 113 decreases monotonically relativeto the angle of incidence θ₁ of imaging light L, so that the angle γ ofthe plane of incidence 113 a of each unit prism 113 tends to becomenegative in the area on the screen plane in which the angle of incidenceθ₁ of imaging light L is great (the area on the side distant from thecenter O of the concentric circles). The conditions under which theplane of incidence 113 a of each unit prism 113 does not get reversetapered when the angle θ₄ at which imaging light L travels in the totalreflection prism lens 114 is nearly equal to 0 are given by thefollowing formula (4):cos⁻¹{cos(θ₁)/n}/2≦λ.  (4)

On the other hand, in the area on the screen plane in which the angle ofincidence θ₁ of imaging light L is small (the area on the side close tothe center O of the concentric circles), part of imaging light Lincident on the plane of incidence 113 a of each unit prism 113 is nottotally reflected at the plane of total reflection 113 b and passesthrough this plane to become stray light.

In order to explain how stray light is produced in each unit prism 113,basic imaging light L₀ that has been refracted at the plane of incidence113 a of the unit prism 113 and then travels toward the very base of theunit prism 113 (i.e., imaging light that passes through the boundarybetween the part of one unit prism 113, imaging light L that has passedthrough this part becoming stray light, and the other part of the unitprism 113, imaging light L that has passed through this part becominguseful light) will now be reviewed.

When the angle of incidence at which imaging light L is incident on theplane of incidence 113 a of each unit prism 113 is denoted by θ₂; theangle at which the imaging light L is refracted at the plane ofincidence 113 a of the unit prism 113, by θ₃; the prism pitch of theunit prisms 113, by p; the width of the part in which the imaging lightL is totally reflected at the plane of total reflection 113 b of theunit prism 113 and is suitably used as useful light, by e₁; the width ofthe part in which the imaging light L is not totally reflected at theplane of total reflection 113 b of the unit prism 113 and passes throughthis plane to become stray light, by e₂; the height of the unit prism113, by h; and the height of the boundary between the part of the planeof incidence 113 a of the unit prism 113, in which the imaging light Lthat has passed through this part becoming stray light, and the otherpart of the plane of incidence 113 a of the unit prism 113, in which theimaging light L that has passed through this part becoming useful light,by s, the width e₁ of the part in which the imaging light L becomesuseful light is given by the following Eq. (5):e ₁=(h−s)×(tan(φ+λ−π/2)+tan θ₁).  (5)

h and s in the above Eq. (5) are given by the following Eqs. (6) and(7), respectively:h=p×tan(φ+λ)×tan φ/(tan(φ+λ)−tan φ);  (6)s=−p×tan(φ+λ)/(1+tan(φ+λ)×tan(φ+λ+θ₃)),  (7)where θ₃=sin⁻¹{sin(θ₁+φ+λ)/n}.  (8)

As is clear from FIG. 3, the relationship between the prism pitch p andthe width e₁ of the part in which imaging light L becomes useful lightis e₁≦p. Further, the ratio e₁/p of the width e₁ of the part in whichimaging light L becomes useful light to the lens pitch p increases asthe angle of incidence θ₁ of imaging light L increases, and at a certainpoint, e₁ becomes equal to p. In this case, in the region in which theangle of incidence θ₁ of imaging light L is greater than that at thepoint at which e₁=p, imaging light L incident on the plane of incidence113 a of the unit prism 113 is totally reflected at the plane of totalreflection 113 b, and no stray light exists.

As explained above, the area on the screen plane in which the angle ofincidence θ₁ of imaging light L is small (the area on the side close tothe center O of the concentric circles) has the problem that part ofimaging light L incident on the plane of incidence 113 a of each unitprism 113 is not totally reflected at the plane of total reflection 113b and passes through this plane to become stray light, while the area onthe screen plane in which the angle of incidence θ₁ of imaging light Lis great (the area on the side distant from the center O of theconcentric circles) has the problem that the plane of incidence 113 a ofeach unit prism 113 gets reverse tapered.

FIG. 4 is a diagram for explaining the relationship between the apicalangle λ of each unit prism 113 and the angle of incidence θ₁ of imaginglight L in the total reflection prism lens 114 of the projection screen111 shown in FIG. 1.

In FIG. 4, line 205 shows the boundary of production of stray light ineach unit prism 113, defined by the above Eq. (5) to Eq. (8), in thecase where the angle θ₄ at which imaging light L travels in the totalreflection prism lens 114 (i.e., the angle of emergence θ₅ at whichimaging light L emerges from the total reflection prism lens 114) is 0;and line 206 shows the boundary of formation of a reverse tapered planeof incidence 113 a of each unit prism 113, defined by the above Eq. (4),in the same case. These lines 205 and 206 are obtained under thecondition that the refractive index n of the material for the totalreflection prism lens 114 is 1.55.

In the inner region surrounded by the two lines 205 and 206 in FIG. 4,there are no such problems that part of imaging light L incident on theplane of incidence 113 a of each unit prism 113 is not reflected at theplane of total reflection 113 b and passes through this plane to becomestray light and that the plane of incidence 113 a of each unit prism 113gets reverse tapered. Therefore, as long as the apical angle λ of eachunit prism 113 and the angle of incidence θ₁ of imaging light L thatvaries according to the position of the unit prism 113 on the screenplane are present in this region, neither the stray light problem northe reverse tapered plane problem occurs. Specifically, for example, inthe case where the unit prisms 113 have a fixed apical angle of 35°, ifthe angle of incidence θ₁ of imaging light L is in the range of 45 to60°, neither the stray light problem nor the reverse tapered planeproblem occurs (see reference numeral 207).

In recent years, there is the trend to make the projection screen 111larger, and in line with this trend, the range of the angle of incidenceθ₁ of imaging light L has increased. Therefore, if the unit prisms 113have a fixed apical angle λ, the angle of incidence θ₁ of imaging lightL tends to get out of the inner region surrounded by the lines 205 and206 in both the area on the screen plane in which the angle of incidenceθ₁ of imaging light L is small and the area on the screen plane in whichthe angle of incidence θ₁ of imaging light L is great.

To overcome the stray light problem in the above-described case, it iseffective to lower the lower limit of the allowable range of the angleof incidence θ₁ of imaging light L, defined by the line 205. To attainthis, it is preferable that the unit prisms 113 situated in the area onthe screen plane in which the angle of incidence θ₁ of imaging light Lis small (the area on the side close to the center O of the concentriccircles) be made to have smaller apical angles λ. On the other hand, toovercome the reverse tapered plane problem, it is effective to raise theupper limit of the allowable range of the angle of incidence θ₁ ofimaging light L, defined by the line 206. To attain this, it ispreferable that the unit prisms 113 situated in the area on the screenplane in which the angle of incidence θ₁ of imaging light L is great(the area on the side distant from the center O of the concentriccircles) be made to have greater apical angles λ.

For this reason, in this embodiment, the unit prisms 113 are, over theentire screen plane, made to have apical angles λ continuously varyingso that the apical angles λ on the side distant from the center O of theconcentric circles are greater than the apical angles λ on the sideclose to the center O of the concentric circles (see reference numerals201 to 203). By this, it is possible to increase the allowable range ofthe angle of incidence θ₁ of imaging light L, and is thus possible tomake the entire screen plane free from both the stray light problem andthe reverse tapered plane problem. Lines 201 to 203 in FIG. 4 showvariations in the apical angle λ of the unit prism 113 in terms of theangle of incidence θ₁ of imaging light L. It is, however, a matter ofcourse that variation in the apical angle λ of the unit prism 113 canalso be shown in terms of the position of the unit prism 113 (thedistance from the center O of the concentric circles), and this is asshown in FIG. 5.

In the above-described embodiment, it is preferable that the plane ofincidence 113 a of each unit prism 113 has a draft angle of 0° or more(preferably 1/1000° or more) to the perpendicular (normal) to the screenplane (the inclination with which the angle γ between the plane ofincidence 113 a and the normal to the screen plane is positive).Further, it is preferable that the surface roughness of the planes ofincidence 113 a of the unit prisms 113 is uniform over the entire screenplane.

(First Modification)

The above embodiment has been described with reference to the case wherethe apical angles λ of the unit prisms 113 are varied continuously overthe entire screen plane. The present invention is not limited to this,and the apical angles λ of the unit prisms 113 may also be variedstep-wise within the screen plane.

The first modification of the projection screen 111 shown in FIGS. 1 to5 will be described with reference to FIGS. 6A, 6B, 7 and 8. Since thebasic construction of this first modification is the same as that of theprojection screen 111 shown in FIGS. 1 to 5, emphasis is, in thefollowing description, laid on those points distinct from the projectionscreen 111 shown in FIGS. 1 to 5.

FIG. 6A is a view of a projection screen 111 according to the firstmodification, viewed from the incident side of the screen, and FIG. 6Bis a view of the projection screen 111 according to the firstmodification (and a projection optical system 112), viewed from the sideof the screen.

As shown in FIGS. 6A and 6B, the projection screen 111 according to thefirst modification comprises a total reflection prism lens 114A having aplurality of unit prisms formed on its back surface (the outermost planeof incidence) side from which imaging light L enters, and, on theviewer's side of the total reflection prism lens 114A, a lenticular lens115.

As in the case of the total reflection prism lens 114 in the projectionscreen 111 shown in FIGS. 1 to 5, the unit prisms of the totalreflection prism sheet 114A concentrically extend around the center O ofthe concentric circles that is not on the screen plane. Further, theprojection optical system 112 is placed at the same height as that ofthe center O of the concentric circles that is not on the screen plane,as shown in FIG. 6B.

The total reflection prism lens 114A is divided into three areas A1, A2and A3 according to the distance from the center O of the concentriccircles.

Of these areas, the area A1 is a first apical-angle-fixed area situatedin the position closer to the center O of the concentric circles thandistance r1 from the center O of the concentric circles, and, in thisarea, the apical angles λ of the unit prisms are fixed at λ1 (firstangle).

The area A2 is a second apical-angle-fixed area situated in the positionmore distant from the center O of the concentric circles than distancer2 from the center O of the concentric circles, and, in this area, theapical angles λ of the unit prisms are fixed at λ2 (second angle). If λ1and λ2 are compared, λ2 is greater than λ1 (λ2>λ1).

The area A3 is an apical-angle-varying area situated between the areasA1 and A2 (in the position more distant from the center O of theconcentric circles than distance r1 from the center O of the concentriccircles, and closer to the center O of the concentric circles thandistance r2 from the center O of the concentric circles), and, in thisarea, the unit prisms have apical angles λ varying between λ1 and λ2with the position on the screen plane.

FIG. 7 shows how the apical angles λ of the unit prisms vary in theareas A1, A2 and A3.

In the area A3, the apical angles λ of the unit prisms gradually varyfrom λ1 to λ2 as the angle between the plane of incidence (see referencenumeral 113 a in FIG. 3) of the unit prism and the screen planegradually varies, with the angle between the plane of total reflectionof the unit prism (see reference numeral 113 b in FIG. 3) and the screenplane remaining unchanged.

If only the areas A1 and A2 are provided without providing the area A3,the apical angles λ of the unit prisms are to sharply vary from λ1 to λ2at a certain point on the screen plane. In this case, not only theapical angles λ of the unit prisms but also the angles of the planes oftotal reflection of the unit prisms (lens angles φ) are, of course, tovary sharply. In particular, with respect to variation in the lens angleφ of the unit prism, the lens angles φ of the unit prisms that aregradually getting smaller as the position of the unit prism varies fromthe side close to the center O of the concentric circles to the sidedistant from this center O sharply vary at the point. There is thereforea possibility that the boundary between the two areas A1 and A2 isunfavorably observed when the produced image is viewed.

On the contrary, in the above-described first modification, the area A3in which the unit prisms have apical angles λ varying between λ1 and λ2with the position on the screen plane is provided between the areas A1and A2 in which the unit prisms have apical angles λ fixed at λ1 and λ2,respectively, so that the variation in the apical angle λ of the unitprism becomes continuous. Further, in the area A3, the unit prisms aremade to have apical angles λ that are varied by varying the anglebetween the plane of incidence of the unit prism and the screen planewithout varying the angle between the plane of total reflection of theunit prism and the screen plane (lens angle φ), so that there is nopossibility that the variation in the angle of the plane of totalreflection is partly retrogressed.

FIG. 8 is a diagram specifically showing the relationship between theangle of incidence θ₁ of imaging light L and the lens angle φ of eachunit prism in the total reflection prism lens 114A in the case where theangle θ₄ at which imaging light L travels in the total reflection lens114A is 0 (i.e., the angle of emergence θ₅ at which imaging light Lemerges from the total reflection prism lens 114A is 0).

Now suppose, as shown in FIG. 8, that the apical angle λ of each unitprism in the area A1 situated on the side close to the center O of theconcentric circles is λ1 (=35°) and that the apical angle λ of each unitprism in the area A2 situated on the side distant from the center O ofthe concentric circles is λ2 (=45°). In this case, if the apical angle λof the unit prism is sharply varied when the angle of incidence θ₁ is52.5°, the angle of the plane of total reflection (lens angle φ), whichis gradually getting smaller as the position of the unit prism getsfarther in the direction from the side close to the center O of theconcentric circles to the side distant from this center O, sharplyincreases by 2.6° at this point (see reference numeral 208). Therefore,there is a possibility that this boundary is unfavorably observed whenthe produced image is viewed.

On the contrary, in the above-described first modification, the apicalangle λ of the unit prism is, for example, varied from λ1 (=35°) to λ2(=45°) by varying, in the region in which the angle of incidence θ₁ ofimaging light L is between 52.5° and 59.2°, only the angle of the planeof incidence of each unit prism, with the angle of the plane of totalreflection of each unit prism (lens angle φ) fixed at 57°, as shown bythe solid line in FIG. 8 (see reference numeral 209). Therefore, thereis no possibility that the variation in the angle of the plane of totalreflection of each unit prism is partly retrogressed.

(Second Modification)

Next, the second modification of the projection screen 111 shown inFIGS. 1 to 5 will be described with reference to FIGS. 9A, 9B and 10.The second modification is a further modification of the above-describedfirst modification, which can further ensure that the variation in theapical angle λ of each unit prism is not perceived. Since the basicconstruction of the second modification is the same as that of the firstmodification described above, emphasis is, in the following description,laid on those points distinct from the first modification.

FIG. 9A is a view of a projection screen 111 according to the secondmodification, viewed from the incident side of the screen, and FIG. 9Bis a view of the projection screen 111 according to the secondmodification (and a projection optical system 112), viewed from the sideof the screen.

As shown in FIGS. 9A and 9B, the projection screen 111 comprises a totalreflection prism lens 114B having a plurality of unit prisms formed onits back surface (the outermost plane of incidence) on which imaginglight L is incident, and, on the viewer's side of the total reflectionprism lens 114B, a lenticular lens 115.

As in the case of the total reflection prism lens 114 of the projectionscreen 111 shown in FIGS. 1 to 5, the total reflection prism lens 114Bconcentrically extends around the center O of the concentric circlesthat is not on the screen plane. Further, the projection optical system112 is placed at the same height as that of the center O of theconcentric circles that is not on the screen plane, as shown in FIG. 9B.

The total reflection prism lens 114B includes areas A1′, A2′ and A3′that correspond to the areas A1, A2 and A3 in the above-described firstmodification, respectively.

Namely, the area A1′ is a first apical-angle-fixed area situated in theposition closer to the center O of the concentric circles than distancer1 from the center O of the concentric circles, and, in this area, theunit prisms have apical angles λ that are fixed at λ1 (first angle).

The area A2′ is a second apical-angle-fixed area situated in theposition more distant from the center O of the concentric circles thandistance r2 from the center O of the concentric circles, and, in thisarea, the unit prisms have apical angles λ that are fixed at λ2 (secondangle). If λ1 and λ2 are compared, λ2 is greater than λ1 (λ2>λ1).

The area A3′ is a first apical-angle-varying part situated between theareas A1′ and A2′ (in the position more distant from the center O of theconcentric circles than distance r1 from the center O of the concentriccircles, and closer to the center O of the concentric circles thandistance r2 from the center O of the concentric circles), and, in thisarea, the unit prisms have apical angles λ varying between λ1 and λ2with the position on the screen plane.

Area A4 with a predetermined width is provided at the boundary betweenthe areas A1′ and A3′, and area A5 with a predetermined width is alsoprovided at the boundary between the areas A3′ and A2′. For this reason,the areas A1′, A2′ and A3′ in the second modification are narrower thanthe areas A1, A2 and A3 in the first modification, respectively, due tothe existence of the areas A4 and A5.

The area A4 is a second apical-angle-varying part situated between theareas A1′ and A3′, and, in this area, the unit prisms have apical anglesλ varying with the position on the screen plane.

The area A5 is a third apical-angle-varying part situated between theareas A3′ and A2′, and, in this area, the unit prisms have apical anglesλ varying with the position on the screen plane.

The area A3′ that is the first apical-angle-varying part, the area A4that is the second apical-angle-varying part, and the area A5 that isthe third apical-angle-varying part constitute the apical-angle-varyingarea.

FIG. 10 shows how the apical angles λ of the unit prisms vary in theareas A1′, A2′, A3′, A4 and A5.

In the area A3 in the above-described first modification, the unitprisms have apical angles λ that vary gradually from λ1 to λ2 as theangle between the plane of incidence (see reference numeral 113 a inFIG. 3) of the unit prim and the screen plane gradually varies, with theangle between the plane of total reflection (see reference numeral 113 bin FIG. 3) and the screen plane remaining unchanged. However, even inthis case, the variations in the angle of the plane of total reflection(lens angle φ) are great at the boundaries between the areas A3 and A1and between the areas A3 and A2 as compared with the other parts. Thereis therefore a possibility that, depending on the design of the shape ofeach unit prism, the boundaries between these areas are clearly observedwhen the produced image is viewed.

For this reason, in the second embodiment, the areas A4 and A5 withpredetermined widths are provided at the boundaries between the areas A3and A1 and between the areas A3 and A2, respectively, and, in theseareas A4 and A5, the apical angle λ of each unit prism is varied byvarying not only the angle between the plane of incidence and the screenplane but also the angle between the plane of total reflection and thescreen plane (lens angle φ). By this, it is possible to make thevariation in the angle of the plane of total reflection smooth, and isthus possible to prevent the boundaries between the above areas frombeing clearly observed when viewing the produced image, thereby makingthe image appear less uneven.

Preferably, in the second modification, the variation in the anglebetween the screen plane and the plane of total reflection (lens angleφ) in the areas A1′, A2′ and A3′ is expressed by a numerical formula,and this numerical formula is subjected to spline interpolation in amanner as shown in Example 5 that will be described later, therebydetermining the degree of change in the angle of the plane of totalreflection in the areas A4 and A5.

Second Embodiment

Next, a projection display comprising a projection screen according tothe second embodiment of the present invention will be described withreference to FIGS. 11 to 13. The second embodiment of the presentinvention is the same as the first embodiment described above exceptthat the construction of the lenticular lens is different from that ofthe lenticular lens in the first embodiment and that the totalreflection prism lens and the lenticular lens are integrally made as onesheet. In the second embodiment of the present invention, partscorresponding to those in the aforementioned first embodiment areindicated by like reference numerals, and detailed descriptions forthese parts are omitted.

As shown in FIG. 11, a projection display 100′ according to the secondembodiment of the present invention comprises a projection screen 111′,and a projection optical system 112 from which imaging light L isobliquely projected on the projection screen 111′.

The projection screen 111′ is for letting imaging light L obliquelyprojected from the projection optical system 112 placed at its rear sideemerge toward the viewer's side, and comprises a total reflection prismlens 114′, and a lenticular lens 115′ provided on the viewer's side ofthe total reflection prism lens 114′.

Of these components, the total reflection prism lens 114′ is forrefracting and condensing imaging light L projected from the projectionoptical system 112, and, as shown in FIG. 12, comprises a base sheet 23and a plurality of unit prisms 113 formed on the incident side surfaceof the base sheet 23 (the outermost plane of incidence on which imaginglight L is incident). As in the above-described first embodiment, eachunit prism 113 has a plane of incidence (first plane) 113 a thatrefracts incident light, and a plane of total reflection (second plane)113 b that totally reflects the light refracted at the plane ofincidence 113 a. Further, the unit prisms 113 are formed as prisms inthe shape of circular arcs extending concentrically around the center Oof the concentric circles that is not on the screen plane (see FIG. 11),and have apical angles λ varying with the position on the screen plane.In particular, it is preferable that the unit prisms 113 have apicalangles λ continuously varying from 30° to 45° so that the apical anglesλ on the side distant from the center O of the concentric circles (theupper side in the figure) are greater than the apical angles λ on theside close to the center O of the concentric circles (the lower side inthe figure). The apical angles λ of the unit prisms 113 may vary in thesame various fashions as in the above-described first embodiment (FIGS.5, 7 and 10, etc.).

On the other hand, the lenticular lens 115′ is provided on the emergentside surface of the base sheet 23, as shown in FIGS. 12 and 13, and hasa plurality of trapezoidal portions 25 with trapezoidal cross sections(unit lenses).

The trapezoidal portions 25 are arranged so that the lower base andupper base of each trapezoid face to the incident side and the emergentside, respectively, and, between each two neighboring trapezoidalportions 25, V-shaped portions 26 with V-shaped cross sections areprovided. The trapezoidal portions 25 are made from a material having apredetermined refractive index. Further, the V-shaped portions 26 areformed by filling the spaces between each two trapezoidal portions 25with a material having a refractive index that is lower than therefractive index of the material for the trapezoidal portions 25,whereby the interfaces between the trapezoidal portions 25 and theV-shaped portions 26 provided between each two neighboring trapezoidalportions 25 can totally reflect and diffuse imaging light L (see FIGS.12 and 13).

Further, it is preferable that the V-shaped portions 26 have thelight-absorbing property of absorbing light that enters these portionsfrom the viewer's side. Although any material can be used for theV-shaped portions 26, it is preferable to make them by the use of, forexample, a mixture of a synthetic resin having a low refractive indexand light-absorbing particles consisting of a dye, a pigment, coloredresin fine particles, or the like.

In the projection screen 111′ shown in FIGS. 11 to 13, imaging light Lobliquely projected from the projection optical system 112 is incidenton the plane of incidence 113 a of each unit prism 113 of the totalreflection prism lens 114′.

The imaging light L incident on the plane of incidence 113 a of eachunit prism 113 is refracted at this plane and then totally reflected atthe plane of total reflection 113 b, and the totally reflected lighttravels in the direction almost vertical to the screen plane towards theviewer's side.

Thereafter, the imaging light L thus emerging from the total reflectionprism lens 114′ is incident on the lower base side of the trapezoidalportions 25 of the lenticular lens 115′; part of this incident lightpasses through the lenticular lens 115′ as it is, while the remainingpart of the incident light is totally reflected at the interfacesbetween the trapezoidal portions 25 and the V-shaped portions 26, andeventually, all of the light emerges from the upper base side of thetrapezoidal portions 25 towards the viewer's side.

Thus, according to the first and second embodiments of the presentinvention, in the projection screen 111, 111′ on which imaging light Lis obliquely projected from the projection optical system 112 placed atits rear side, a plurality of unit prisms 113 of the total reflectionprism lens 114, 114A, 114B, 114′ provided at its back surface on whichimaging light L is incident are made to have apical angles λ varyingwithin a certain angle range (e.g., 30° or more and 45° or less) so thatthe apical angles λ on the side distant from the center O of theconcentric circles are greater than the apical angles λ on the sideclose to the center O of the concentric circles. By this, the apicalangles λ of the unit prisms 113 situated in the area on the side closeto the projection optical system 112, in which the angle of incidence θ₁of imaging light L is small, can be made smaller, while the apicalangles λ of the unit prisms 113 situated in the area on the side distantfrom the projection optical system 112, in which the angle of incidenceθ₁ of imaging light L is great, can be made greater. For this reason, itis possible to increase the allowable range of the angle of incidence θ₁of imaging light L that is a range in which imaging light L loss due tothe production of stray light is not caused, and there can thus beobtained the projection screen 111, 111′ and the projection display 100,100′ that can display, without undergoing lowering of surface brightnessor contrast, an image with high quality comparable to an image obtainedwhen imaging light L is projected on a projection screen nearlyvertically from a projection optical system 112.

Further, according to the first and second embodiments of the presentinvention, the first apical-angle-fixed area A1 in which the unit prisms113 have apical angles λ fixed at a predetermined first angle λ1, thesecond apical-angle-fixed area A2 whose location is different from thatof the first apical-angle-fixed area A1 and in which the unit prisms 113have apical angles λ fixed at a predetermined second angle λ2 that isdifferent from the first angle λ1, and the apical-angle-varying area A3situated between the first and second apical-angle-fixed areas A1 and A2and in which the unit prisms 13 have apical angles λ varying between thefirst angle λ1 and the second angle λ2 with the position on the screenplane are, as the first modification, provided on the total reflectionprism lens 114A, so that it is possible to vary the apical angles λ ofthe unit prisms 113 of the total prism lens 114A not over the entirescreen plane but only partly. By this, it becomes easy to make a moldfor use in the molding of the total reflection prism lens 114A, and theprojection screen 111, 111′ and the projection display 100, 100′ thatcan ensure high image quality can thus be produced more inexpensively.

Furthermore, according to the first and second embodiments of thepresent invention, the first apical-angle-varying part A3′ in which theunit prisms 113 have apical angles λ that vary as only the angle betweenthe screen plane and the plane of incidence 113 a varies, with the anglebetween the screen plane and the plane of total reflection 113 bremaining unchanged, and the second and third apical-angle-varying partsA4 and A5 situated between the first apical-angle-varying part A3′ andthe first apical-angle-fixed area A1′ and between the firstapical-angle-varying part A3′ and the second apical-angle-fixed areaA2′, respectively, in which the unit prisms 113 have apical angles λthat vary as both the angle between the screen plane and the plane ofincidence 113 a and the angle between the screen plane and the plane oftotal reflection 113 b vary are, as the second modification, provided inthe apical-angle-varying area on the total reflection prism lens 114B,so that it is possible to make the boundaries between the above areasmore unclear. Image quality higher than that obtained by the firstmodification can thus be attained.

Furthermore, according to the first and second embodiments of thepresent invention, since the plane of incidence 113 a of each unit prism113 has a draft angle of 0° or more to the perpendicular (normal) to thescreen plane, the mold for use in the molding of the unit prisms 113includes no reverse tapered portions. Therefore, it becomes easy to makethe mold, and, moreover, the unit prisms 113 can be easily released fromthe mold in the lens molding process.

Furthermore, according to the first and second embodiments of thepresent invention, since the surface roughness of the planes ofincidence 113 a of the unit prisms 113 is uniform over the entire screenplane, it is possible to produce, on the screen plane, an image with nounevenness; a high-quality image can thus be viewed.

(Other Embodiments)

The present invention is not limited to the above-described first andsecond embodiments and can be modified or altered variously as describedunder the following items from (1) to (6). These modifications andalternations also are within the scope of the present invention.

(1) In the above-described first and second embodiments, the totalreflection prism lens 114, 114A, 114B, 114′ and the lenticular lens 115,115′ are used as a total reflection prism lens and a lenticular lens,respectively. However, as for the concrete shapes of the totalreflection prism lens, the lenticular lens and the others, any otherconstruction may also be adopted as long as it meets the characteristicfeatures of the present invention as described above.

(2) In the above-described first embodiment, although the totalreflection prism lens 114, 114A, 114B, 114′ and the lenticular lens 115,115′ are made as separate sheets (a prism sheet and a lenticular lenssheet), they may also be made integrally as one sheet. On the otherhand, in the above-described second embodiment, although the totalreflection prism lens 114′ and the lenticular lens 115′ are madeintegrally as one sheet, they may also be made as separate sheets (aprism sheet and a lenticular lens sheet).

(3) In the above-described first and second embodiments, a diffusingsheet for diffusing imaging light L that has passed through the totalreflection prism lens 114, 114A, 114B, 114′ and the lenticular lens 115,115′ may be provided in the position indicated by reference numeral 117in FIGS. 1 and 11, on the viewer's side of the lenticular lens 115, 115′(on the viewer's side of the total reflection prism lens 114, 114A,114B, 114′ if the lenticular lens 115, 115′ is not present). Thediffusing sheet is preferably a sheet in which a diffusing agent or thelike is incorporated in order to impart diffusing properties to thesheet.

(4) In the above-described first and second embodiments, although thelenticular lens 115, 115′ is provided on the viewer's side of the totalreflection prism lens 114, 114A, 114B, 114′, a diffusing sheet thatdiffuses light by a diffusing agent or the like, a beads screen coatedwith a plurality of beads that diffuse light by means of refraction oflight, or the like may also be used instead of the lenticular lens 115,115′.

(5) In the above-described first and second embodiments, a functionallayer may also be provided in the position indicated by referencenumeral 117 in FIGS. 1 and 11, on the viewer's side of the lenticularlens 115, 115′ (on the viewer's side of the total reflection prism lens114, 114A, 114B, 114′ if the lenticular lens 115, 115′ is not present).A variety of functional layers can be used, and examples of such layersinclude an antireflection layer (AR layer), a hard coat layer (HClayer), an antistatic layer (AS layer), an anti-glaring layer (AGlayer), a stain-resistant layer, and a sensor layer.

The antireflection layer (AR layer) is for restraining the reflection oflight at the projection screen 100, 100′, and can be obtained bylaminating, to a lens surface, a film having the function of restrainingthe reflection of light, or by subjecting a lens surface directly toantireflection treatment. The hard coat layer (HC layer) is forprotecting the surface of the projection screen 100, 100′ fromscratches, and can be obtained by laminating, to a lens surface, awear-resistant film having the reinforcing action, or by subjecting alens surface directly to hard coat treatment. The antistatic layer (ASlayer) is for removing static electricity that occurs on the projectionscreen 100, 100′, and can be obtained by laminating an antistatic filmto a lens surface, or by subjecting a lens surface directly toantistatic treatment. The anti-glaring layer (AG layer) is forpreventing glaring of the projection screen 100, 100′, and can beobtained by laminating, to a lens surface, a film having the function ofpreventing glaring, or by subjecting a lens surface directly toanti-glaring treatment. The stain-resistant layer is for preventing thesurface of the projection screen 100, 100′ from being stained, and canbe obtained by laminating, to a lens surface, a film having the functionof preventing staining, or by subjecting a lens surface tostain-resistant treatment. The sensor layer is a layer that can functionas a touch sensor or the like.

(6) In the projection displays 100, 100′ according to theabove-described first and second embodiments, although the upwardprojection mode in which imaging light L emitted from the projectionoptical system 112 is upwardly projected on the projection screen 111,111′ is adopted, the downward projection mode in which imaging light Lemitted from the projection optical system 112 is downwardly projectedon the projection screen 111, 111′ may also be adopted.

In the case where the upward projection mode is adopted in theprojection display 100, 100′, the projection screen 111, 111′ and theprojection optical system 112 are contained within a cabinet 151 withtheir positional relation as shown in FIG. 14, for example.Specifically, for example, by using an LCD light bulb as an imaginglight source in the projection optical system 112, it is possible toproject, on a 50-inch projection screen 111, 111′, an image from belowthe screen so that the angle of incidence θ₁₁ at which imaging light Lis incident on the bottom of the screen plane is 45° and that the angleof incidence θ₁₀ at which imaging light L is incident on the top of thescreen plane is 60°. In this case, the horizontal distance between theprojection screen 111, 111′ and the projection optical system 112 isapproximately 800 mm.

On the other hand, when the downward projection mode is adopted in theprojection display 100, 100′, the projection screen 111, 111′ and theprojection optical system 112 are contained within a cabinet 152 withtheir positional relation as shown in FIG. 15, for example.Specifically, for example, by using a DMD as an imaging light source inthe projection optical system 112, it is possible to project, on a50-inch projection screen 111, 111′, an image from above the screen sothat the angle of incidence θ₂₀ at which imaging light L is incident onthe top of the screen plane is 45° and that the angle of incidence θ₂₁at which imaging light L is incident on the bottom of the screen planeis 70°. In this case, the horizontal distance between the projectionscreen 111, 111′ and the projection optical system 112 becomesapproximately 700 mm.

In the projection displays 100 and 100′ shown in FIGS. 14 and 15,imaging light L emitted from the projection optical system 112 isprojected directly on the projection screen 111, 111′. However, theprojection screen and the projection optical system may also becontained within a cabinet 153 with their positional relation as shownin FIG. 16 so that imaging light L emitted from the projection opticalsystem 112 is projected on the projection screen 111, 111′ via areflector 155.

EXAMPLES

Specific examples of the aforementioned embodiments will now be givenbelow.

Example 1

A projection screen for use in a 50-inch rear projection typetelevision, comprising a prism sheet and a lenticular lens sheet, wasproduced as a projection screen of Example 1. The projection screen ofExample 1 corresponds to the first embodiment described above.

First of all, by the use of a mold obtained by cutting using an NClathe, an ultraviolet-curing resin (refractive index of the cured resin:1.55) placed on an acrylic base sheet with a thickness of 1.8 mm wascured and shaped, whereby a prism sheet with a total thickness of 2 mm,having a total reflection prism lens on its one surface, was obtained.

In the above process, the total reflection prism lens was formed on theprism sheet so that it had a plurality of prisms (unit prisms) in theshape of circular arcs concentrically extending around the center of theconcentric circles that was not on the screen plane. The radius (thedistance from the center of the concentric circles) of the circular arcof the unit prism at the center of the bottom of the screen plane wasmade 800 mm; the prism pitch was made 100 μm; and the height of the eachprism was made approximately 150 μm. Further, the unit prism situated atthe lower edge of the screen plane (on the side closest to the center ofthe concentric circles) was made to have an apical angle λ of 37°; theunit prism situated at the upper edge of the screen plane (on the sidemost distant from the center of the concentric circles) was made to havean apical angle λ of 40°; and the unit prisms situated between the abovetwo unit prisms were made to have apical angles λ varying from 37° to40° (see FIG. 17). The angle of emergence θ₅ at which imaging lightemerges from each unit prism was made 0 (normal emergence).

Next, by the use of a cylindrical roll mold, a lenticular lens sheet wasprepared by extruding an impact-resistant acrylic resin.

In the above process, a lenticular lens was formed on the lenticularlens sheet so that it had a plurality of unit lenses with half-ellipticcross sections. The transverse diameter of each unit lens was made 140μm, and the longitudinal diameter of each unit lens was made 100 μm.Further, the lens pitch was made 140 μm, and the height of each unitlens was made 50 μm. As a result, the following diffusion propertieswere obtained: the angle of horizontal diffusion was 35° when expressedas half angle, and the angle of vertical diffusion was 15° whenexpressed as half angle.

When making the lenticular lens sheet by extrusion, extremely smallamounts of a black dye and a diffusing agent were incorporated in theimpact-resistant acrylic resin. The lenticular lens sheet thus producedwas found to have a transmittance of 70% and to have the property ofpreventing reflection of extraneous light, etc. and the diffusingeffect.

A projection screen was produced by the combination use of theabove-prepared prism sheet and lenticular lens sheet. The projectionscreen produced in this manner was then incorporated into a projectiondisplay (rear projection type television) of upward projection mode asshown in FIG. 14. The screen size of the projection screen was 50inches, and an LCD light bulb was used as an imaging light source in theprojection optical system. The projection optical system was placed 800mm below the lower edge of the screen plane, and the horizontal distancebetween the projection screen and the projection optical system(projection distance) was made 800 mm. Further, the angle of incidenceθ₁₁ at which imaging light was incident on the bottom of the screenplane was made 45°, and the angle of incidence θ₁₀ at which imaginglight was incident on the center of the top of the screen plane was made60°.

Example 2

A projection screen for use in a 50-inch rear projection typetelevision, comprising a total reflection prism sheet and a lenticularlens sheet that had been integrally made as one sheet, was produced as aprojection screen of Example 2. The projection screen of Example 2corresponds to the second embodiment described above.

First of all, by the use of a mold obtained by cutting using an NClathe, an ultraviolet-curing resin (refractive index of the cured resin:1.55) placed on an acrylic base sheet with a thickness of 1.8 mm wascured and shaped, whereby a prism sheet with a total thickness of 2 mm,having a total reflection prism lens on its one surface, was prepared.

In the above process, the total reflection prism lens was formed on theprism sheet so that it had a plurality of prisms (unit prisms) in theshape of circular arcs concentrically extending around the center of theconcentric circles that was not on the screen plane. The radius (thedistance from the center of the concentric circles) of the circular arcof the unit prism at the center of the bottom of the screen plane wasmade 800 mm; the prism pitch was made 100 μm; and the height of eachprism was made approximately 150 μm. Further, the unit prism situated atthe lower edge of the screen plane (on the side closest to the center ofthe concentric circles) was made to have an apical angle λ of 37°; theunit prism situated at the upper edge of the screen plane (on the sidemost distant from the center of the concentric circles) was made to havean apical angle λ of 40°; and the unit prisms situated between the abovetwo unit prisms were made to have apical angles λ varying from 37° to40° (see FIG. 17). The angle of emergence θ₅ at which imaging lightemerges from each unit prism was made 0 (normal emergence).

Next, on the other surface of the prism sheet prepared in theabove-described manner, a plurality of trapezoidal portions withtrapezoidal cross sections (unit lenses) were formed, and the spacesbetween each two neighboring trapezoidal portions were filled with alow-refractive-index resin containing light-absorbing particles, therebyforming V-shaped portions. An epoxy acrylate having a high refractiveindex was used as the material for the trapezoidal portions. A urethaneacrylate having a low refractive index was used as the material for theV-shaped portions; and RUBCOULEUR (trademark) manufactured byDainichiseika Color & Chemicals Mfg. Co., Ltd., Japan was used as thelight-absorbing particles. RUBCOULEUR had a mean particle diameter of 8μm, and was added in an amount of 45% by weight.

In the above process, the lens pitch of the trapezoidal portions wasmade 50 μm, and the refractive index of these portions was made 1.57.Further, the refractive index of the V-shaped portions was made 1.48.The length of the upper base of each trapezoidal portion and that of thebase of the triangle of the V-shaped portion were made equal to eachother, thereby making the so-called black stripe percentage 50%. Thevertical angle of each V-shaped portion was made 20°.

Thus, the total reflection prism lens and the lenticular lens wereintegrally made as one sheet to give a projection screen. Thisprojection screen was then incorporated, as in Example 1, into aprojection display (rear projection type television) of upwardprojection mode as shown in FIG. 14. The screen size of the projectionscreen was 50 inches, and an LCD light bulb was used as an imaging lightsource in the projection optical system. The projection optical systemwas placed 800 mm below the lower edge of the screen plane, and thehorizontal distance between the projection screen and the projectionoptical system (projection distance) was made 800 mm. Further, the angleof incidence θ₁₁ at which imaging light was incident on the bottom ofthe screen plane was made 45°, and the angle of incidence θ₁₀ at whichimaging light was incident on the center of the top of the screen planewas made 60°.

Example 3

A projection screen of Example 3 was prepared by laminating a 0.1 mmthick AR coat film to the front surface (the outermost surface on theviewer's side) of the lenticular lens in the projection screen ofExample 2.

Example 4

A projection screen of Example 4 was prepared by altering mainly the wayof variation in the apical angle λ of the unit prism of the totalreflection prism lens of the prism sheet in the projection screen ofExample 1. The projection screen of Example 4 corresponds to the firstmodification of the first embodiment described above.

Specifically, in Example 4, a total reflection prism lens was formed onthe prism sheet of the projection screen so that it had a plurality ofprisms (unit prisms) in the shape of circular arcs concentricallyextending around the center of the concentric circles that was not onthe screen plane. The radius (the distance from the center of theconcentric circles) of the circular arc of the unit prism at the centerof the bottom of the screen plane was made 250 mm; and the prism pitchwas made 100 μm. Further, the unit prism situated at the lower edge ofthe screen plane (on the side closest to the center of the concentriccircles) was made to have an apical angle λ of 35°; the unit prismsituated at the upper edge of the screen plane (on the side most distantfrom the center of the concentric circles) was made to have an apicalangle λ of 40°; and the unit prisms situated in the area betweendistance r1 from the center of the concentric circles of 529.6 mm (angleof incidence: 57.3°) and distance r2 from the center of the concentriccircles of 605.9 mm (angle of incidence: 60.7°) were made to have apicalangles λ varying from 35° to 40°. The solid line in FIG. 18 indicatesthe relationship between the position and apical angle λ of each unitprism situated in the vicinity of the area in which the apical angles λof the unit prisms vary.

The lens angles φ of the unit prisms situated in the area betweendistance r1 from the center of the concentric circles of 529.6 mm (angleof incidence: 57.3°) and distance r2 from the center of the concentriccircles r2 of 605.9 mm (angle of incidence: 60.7°) were fixed at 55.25°,as indicated by the solid line in FIG. 19. The angle of emergence θ₅ atwhich imaging light emerges from each unit prism was made 0 (normalemergence).

By the combination use of the prism sheet prepared in theabove-described manner and the same lenticular lens sheet as that inExample 1, a projection screen was produced. The projection screenproduced in this manner was then incorporated into a projection display(rear projection type thin television) of upward projection mode asshown in FIG. 14. The screen size of the projection screen was 55 inches(16:9), and an LCD light bulb was used as an imaging light source in theprojection optical system. The projection optical system was placed 250mm below the lower edge of the screen plane, and the horizontal distancebetween the projection screen and the projection optical system(projection distance) was made 340 mm. Further, the angle of incidencee₁ at which imaging light was incident on the bottom of the screen plane(distance from the center of concentric circles: 250 mm) was made 36.3°,and the angle of incidence θ₁ at which imaging light was incident on thetop corner of the screen plane (distance from the center of theconcentric circles: 1116 mm) was made 73.0°.

Example 5

A projection screen of Example 5 was prepared by altering the way ofvariation in the apical angle λ of the unit prism of the totalreflection prism lens of the prism sheet in the projection screen ofExample 4. The projection screen of Example 5 corresponds to the secondmodification of the first embodiment described above.

The same projection screen as that of Example 4 was prepared as theprojection screen of Example 5, provided that the unit prisms of thetotal reflection prism lens on the prism sheet, situated in the areabetween a distance from the center of the concentric circles of 500 mmand a distance from the center of the concentric circles of 650 mm, weremade to have lens angles φ determined by the use of a splineinterpolation function with a node of 5.

The relationship between the position and apical angle λ of each unitprism in the vicinity of the area in which the apical angles λ of theunit prisms vary is indicated by the dotted line in FIG. 18. Further,the relationship between the position and lens angle φ of each unitprism in the vicinity of the area in which the apical angles λ of theunit prisms vary is indicated by the dotted line in FIG. 19.

The following Eq. (9) was used as the spline interpolation function:$\begin{matrix}{{\phi = {\phi_{1} + {\sum\limits_{k = 1}^{5}\quad{\Delta_{k}\left\lbrack {\left\{ {1 + \left( {1 + \frac{r - r_{k}}{r_{5} - r_{1}}} \right)^{m}} \right\}^{\frac{1}{m}} - 1} \right\rbrack}}}},} & (9)\end{matrix}$where

-   -   Δ₁=(φ₂−φ₁)/a₁,        Δ_(k)=(φ_(k+1)−φ_(k))/a_(k)−(φ_(k)−φ_(k−1))/a_(k−1),    -   in which a_(k)=(r−r_(k))/(r₅−r₁).

The parameters in Eq. (9) were as shown in the table below.

m=32 k 1 2 3 4 5 r 475 500 530 605 640 a 0 0.15152 0.33333 0.78788 1 φ56.3 55.807 55.25 55.25 54.745 Δ −3.2538 0.1903 3.0635 −2.3807 —

After determining the angle of the plane of total reflection of eachunit prism (lens angle φ) by the use of the spline interpolationfunction of the above Eq. (9), the angle of the plane of incidence γ andapical angle λ of the unit prism were calculated by the following Eq.(10):tan γ={cos θ₁(tan φ−sin φ+cos φ)−n(tan φ·sin φ−cos φ)}/{sin θ₁(tan φ·sinφ+cos φ)−2n sin φ},  (10)

-   -   where λ=π/2+γ−φ.

By the combination use of the prism sheet prepared in theabove-described manner and the same lenticular lens sheet as that inExample 1, a projection screen was produced. The projection screen thusproduced was then incorporated, as in Example 4, into a projectiondisplay (rear projection type thin television) of upward projection modeas shown in FIG. 14. The screen size of the projection screen was 55inches (16:9), and an LCD light bulb was used as an imaging light sourcein the projection optical system. The projection optical system wasplaced 250 mm below the lower edge of the screen plane, and thehorizontal distance between the projection screen and the projectionoptical system (projection distance) was made 340 mm. Further, the angleof incidence θ₁ at which imaging light was incident on the center of thebottom of the screen plane (distance from the center of the concentriccircles: 250 mm) was made 36.3°, and the angle of incidence θ₁ at whichimaging light was incident on the top corner of the screen plane(distance from the center of the concentric circles: 1116 mm) was made73.0°.

Comparative Example 1

The procedure of Example 4 was repeated, except that the unit prisms ofthe total prism lens in the projection screen were made to have a fixedapical angle λ of 40°, thereby producing a projection screen ofComparative Example 1.

Comparative Example 2

The procedure of Example 4 was repeated, except that the unit prisms ofthe total prism lens in the projection screen, situated in the area lessthan 544 mm distant from the center of the concentric circles (angle ofincidence: 58.0°), were made to have a fixed apical angle λ of 35°,thereby producing a projection screen of Comparative Example 2.

In the total reflection prism lens in Comparative Example 2, the apicalangles λ of the unit prisms situated in the area more than 544 mmdistant from the center of the concentric circles are negative (λ<0)according to the above-described Eqs. (1) to (3) concerning the totalreflection prism lens. Therefore, in order to let imaging light emergevertically from this area, the planes of incidence of the unit prismssituated in this area were made vertical, and the lens angle φ of theFresnel lens was determined by the following Eq. (11):φ={sin⁻¹(cos θ₁ /n)+π/2}/2.  (11)

In this case, the unit prisms of the total reflection prism lens in theprojection screen of Comparative Example 2, situated in the area morethan 544 mm distant from the center of the concentric circles, are tohave apical angles λ increasing gradually from 35°, and the planes ofincidence of the unit prisms become rough surfaces with flaws createdwhile cutting a mold material.

(Results of Evaluation)

The projection screen of Example 1 was found to have a wide allowablerange of the angle of incidence, and a high-quality image was obtainedwith this projection screen without undergoing lowering of surfacebrightness or contrast. The transmittance was 60%, the reflectance was5%, and the gain was 3. Further, the angle of vertical diffusion(vertical viewing angle) was 10° (half angle), and that of horizontaldiffusion (horizontal viewing angle) was 25° (half angle).

The projection screen of Example 2 was, like the projection screen ofExample 1, found to have a wide allowable range of the angle ofincidence, and a high-quality image was obtained with this projectionscreen without undergoing lowering of surface brightness or contrast.The transmittance was 80%, the reflectance was 5%, and the gain was 4.Further, the angle of vertical diffusion (vertical viewing angle) was12° (half angle), and that of horizontal diffusion (horizontal viewingangle) was 25° (half angle).

The projection screen of Example 3 was, like the projection screen ofExample 2, found to have a wide allowable range of the angle ofincidence, and a high-quality image was obtained with this projectionscreen without undergoing lowering of surface brightness or contrast.This projection screen was also found to have a reflectance improved by1.5% over the projection screen of Example 2.

The projection screens of Examples 4 and 5 were found to have wideallowable ranges of the angle of incidence, and high-quality images wereobtained with these projection screens without undergoing lowering ofsurface brightness or contrast. In particular, the image quality wasuniform over the entire screen planes, and images with extremely highquality were obtained.

On the other hand, in the case of the projection screen of ComparativeExample 1, the central part of the bottom of the screen plane appearedslightly dark as compared with the projection screens of Examples 1 to4, and ghost images were observed.

In the case of the projection screen of Comparative Example 2, theboundary, 544 mm distant from the center of the concentric circles,between the two areas different in the angle of the plane of incidenceof the unit prism and its vicinity were clearly observed.

1. A projection screen that allows imaging light obliquely projectedfrom a projection optical system placed at a rear side of the projectionscreen to emerge toward a viewer's side of the projection screen,comprising: a total reflection prism lens having a plurality of unitprisms provided on its back surface on which imaging light is incident,each of the unit prisms having a first plane that refracts the incidentlight and a second plane that totally reflects the light refracted bythe first plane, wherein each of the unit prisms has an apical anglethat corresponds to an angle between the first and second planes, andthe apical angles of the unit prisms vary with position of each of theunit prisms on a screen plane.
 2. The projection screen according toclaim 1, wherein the unit prisms concentrically extend around a centerof concentric circles that is not on the screen plane.
 3. The projectionscreen according to claim 2, wherein the unit prisms have apical anglesvarying so that the apical angles on a side distant from the center ofthe concentric circles are greater than the apical angles on a sideclose to the center of the concentric circles.
 4. The projection screenaccording to any of claims 1 to 3, wherein the unit prisms have apicalangles varying from 30° to 45°.
 5. The projection screen according toclaim 1, wherein the unit prisms have apical angles that varycontinuously as the position of the unit prism varies from the sideclose to the center of the concentric circles to the side distant fromthis center.
 6. The projection screen according to claim 1, wherein thetotal reflection prism lens has: a first apical-angle-fixed area inwhich the unit prisms have apical angles fixed at a predetermined firstangle; a second apical-angle-fixed area whose location is different fromthat of the first apical-angle-fixed area and in which the unit prismshave apical angles fixed at a predetermined second angle that isdifferent from the first angle; and an apical-angle-varying area that issituated between the first and second apical-angle-fixed areas and inwhich the unit prisms have apical angles varying between the first andsecond angles with the position on the screen plane.
 7. The projectionscreen according to claim 6, wherein the apical-angle-varying areacomprises a first apical-angle-varying part in which the unit prismshave apical angles that vary as only an angle between the first plane ofthe unit prism and the screen plane varies, with an angle between thesecond plane of the unit prism and the screen plane remaining unchanged.8. The projection screen according to claim 7, wherein theapical-angle-varying area further comprises a secondapical-angle-varying part that is situated between the firstapical-angle-varying part and the first apical-angle-fixed area and inwhich the unit prisms have apical angles that vary as both an anglebetween the first plane of the unit prism and the screen plane and anangle between the second plane of the unit prism and the screen planevary; and a third apical-angle-varying part that is situated between thefirst apical-angle-varying area and the second apical-angle-fixed areaand in which the unit prisms have apical angles that vary as both anangle between the first plane of the unit prism and the screen plane andan angle between the second plane of the unit prism and the screen planevary.
 9. The projection screen according to claim 1, wherein the firstplane of each of the unit prisms has a draft angle of 0° or more to theperpendicular to the screen plane.
 10. The projection screen accordingto claim 1, wherein the first planes of the unit prisms have surfaceroughness that is uniform over the entire screen plane.
 11. Theprojection screen according to any of claims 1 to 10, further comprisinga lenticular lens for diffusing light that has passed through the totalreflection prism lens, provided on a viewer's side of the totalreflection prism lens.
 12. The projection screen according to claim 11,wherein the lenticular lens has a plurality of unit lenses withhalf-elliptic cross sections.
 13. The projection screen according toclaim 11, wherein the lenticular lens has a plurality of unit lenseswith trapezoidal cross sections.
 14. The projection screen according toclaim 13, wherein the unit lenses with trapezoidal cross sections arearranged so that the lower base and upper base of each trapezoid face tothe incident side and the emergent side, respectively; portions withV-shaped cross sections are created between each two neighboring unitlenses; the unit lenses are made from a material having a predeterminedrefractive index; those portions created between each two neighboringunit lenses are made from a material having a refractive index that islower than that of the material for the unit lenses; and the interfacesbetween the unit prisms and the portions created between each twoneighboring unit prisms allow light to be totally reflected.
 15. Theprojection screen according to claim 14, wherein the portions withV-shaped cross sections have the light-absorbing property of absorbinglight entering from the viewer's side of the projection screen.
 16. Theprojection screen according to claim 15, wherein the portions withV-shaped cross sections are made from a resin mixed with light-absorbingparticles.
 17. The projection screen according to claim 11, wherein thetotal reflection prism lens and the lenticular lens are integrally madeas one sheet.
 18. The projection screen according to claim 1, furthercomprising a diffusing sheet for diffusing light that has passed throughthe total reflection prism lens, provided on a viewer's side of thetotal reflection prism lens.
 19. The projection screen according toclaim 11, further comprising a diffusing sheet for diffusing light thathas passed through both the total reflection prism lens and thelenticular lens, provided on a viewer's side of the lenticular lens. 20.The projection screen according to claim 1, further comprising afunctional layer comprising at least one layer selected from the groupconsisting of an antireflection layer, a hard coat layer, an antistaticlayer, an anti-glaring layer, a stain-resistant layer, and a sensorlayer.
 21. A projection display comprising: a projection screen as setforth in claim 1; and a projection optical system for obliquelyprojecting imaging light on the projection screen.
 22. A totalreflection prism sheet for use in a projection screen that allowsimaging light obliquely projected from a projection optical systemplaced at a rear side of the projection screen to emerge toward aviewer's side of the projection screen, comprising: a total reflectionprism lens having a plurality of unit prisms provided on its backsurface on which imaging light is incident, each of the unit prismshaving a first plane that refracts incident light and a second planethat totally reflects the light refracted at the first plane, whereineach of the unit prisms has an apical angle that corresponds to an anglebetween the first and second planes, and the apical angles of the unitprisms vary with position of each of the unit prisms on a screen plane.